Question

A person standing between two parallel hills fores a gun. He hears the first echo after 3/2 s, and second echo after 5/2 s. If speed of sound is 332 m/s, calculate the distance between the hills. When will hear the third echo ?

Answer 1

Let $d$ be the distance of first hill , which gives an echo after $3/2s$ and $d^{\prime }$ be the distance of another hill which gives echo after $5/2s$ , from the person .

given , speed of sound $=332m/s$

now for echo from first hill ,

total distance travelled by sound $=2d$ , (distance is doubled as the sound comes back to person after reflection)

total time taken by sound $=3/2s$ , to travel a distance of $2d$,

hence , distance=speed$\times$time ,

$2d=332\times \left(3/2\right)$ ,

or $d=249m$ ,

for echo from another hill ,

total distance travelled by sound $=2d^{\prime }$ , (distance is doubled as the sound comes back to person after reflection)

total time taken by sound $=5/2s$ , to travel a distance of $2d^{\prime }$,

hence , distance=speed$\times$time ,

$2d^{\prime }=332\times \left(5/2\right)$ ,

or $d^{\prime }=415m$ ,

therefore total distance between hills $=249+415=664m$ .

Third echo will be heard when sound coming to person after reflection from first hill (first echo) goes toward another hill and reflects back to person again ,

time taken by sound to reflect back to person from first hill (first echo) $=3/2s$ ,

time taken by sound to reflect back to person from another hill $=5/2s$ ,

therefore , total time (for third echo) $=\left(3/2\right)+\left(5/2\right)=4s$ .